Gender has nothing to do with offspring or sexual reproduction and everything to the way societies have constructed gender roles. Once again, there is nothing inherently biological in the formation or proscription of gender roles.
Hell, if gender roles were as linked to reproduction in humans as you suggest, we would all trace our lineage matrilinearly, and monogamy would not be the norm. The dominance of patrilineage and monogamy suggest that there absolutely no link between society's constructed gender roles and any biological imperative regarding reproduction.
One of those was admittedly a hyperbole that I should have face-checked and corrected before posting; that's on me. That said, at least I'm appealing to those who would be considering authorities on the subject. You simply keep re-asserting that biology and gender are inextricably, as if these were simply common sense and not concepts obviously in dispute, with little attempt to back it up and absolutely no evidence that such a belief is backed by any sort of scientific community. If you have any -modern- studies to link to, please share them. I'm always happy to learn.
If a speak with a sense of confidence, I do so not because I have faith, but because I have the knowledge, study, and experience to understand what it is I am talking about. This is only an example of "belief" or "faith" in the sense that I have greater "faith" in academic research than I do in what appears to be your "gut" feel for "common sense".